AA max value on Q626 3-way

CO is a probably winning-ish reg 14-10 who only 3bets AA, his fold to cbet is low 38% and he's kinda floaty (80% bet flop/turn vs missed c-bets). He won't be flatting a set on a two-tone board (notes, decent sample). BB is 21-10 passive fish who will play faceup and obviously calls too much.

ok, flop is interesting. CO's calling range is something like 77-JJ/KQs/AQ/KK on this flop, although i expect him to raise KK. He doesn't have any flush draws in his range cos pre and i block with the flush ace. BB is calling all sorts of dumb top pair/77-JJ/weak flush draw types of hands and never has anything strong.

Turn is interesting. Like, I should probably be check-shoving right? I think he's betting all of his hands that beat TT if i check, and he seems to think that i don't fire barrels light (probably true). Once he bets and i shove he may level himself into calling vs my face-up AsKs....
or is this just me being ridiculous and it's time to bet $5.80 or something?

Full Tilt No-Limit Hold'em, $0.25 BB (9 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

CO ($25)
Button ($28.85)
SB ($26.59)
BB ($25)
UTG ($22.77)
UTG+1 ($17.25)
MP1 ($25)
Hero (MP2) ($30.22)
MP3 ($21.20)

Preflop: Hero is MP2 with A, A
3 folds, Hero bets $0.85, 1 fold, CO calls $0.85, 2 folds, BB calls $0.60

Flop: ($2.65) 2, 6, Q (3 players)
BB checks, Hero bets $1.80, CO calls $1.80, BB calls $1.80

Turn: ($8.05) 6 (3 players)
BB checks, time to fps check = shove da nutz?

{Edit: Fixed the title; before it said "AA max value on Q622 3-way". --spoonitnow}